# A Horse Herd Optimization Algorithm (HOA)-Based MPPT Technique under Partial and Complex Partial Shading Conditions

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## Abstract

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## 1. Introduction

#### 1.1. Prior Works

#### 1.2. Contribution

- Its superiority is underlined by the experimental results and, since only one parameter is used for the exploration and exploitation phase it results, in terms of quick tracking, in almost zero oscillations.
- The HOA particles are able to remain stationary and the oscillation becomes equal to zero when a cycle of iteration ends, and the power converging efficiency is approximately 99.1%. The absence of this characteristic in PSO and ACS, etc. results in the loss of power and unwanted oscillations.
- The comparison between the HOA and the existing scheme is performed under four different scenarios of weather conditions. The HOA technique can harvest maximum energy under PS and CPS. Moreover, the results of tracking the MPP under different PS and CPS scenarios are represented in the experimental part of this paper, which clearly shows that the HOA technique performs better with respect to convergence rate and zero oscillation, as well as fast-tracking in comparison to P&O, InC, PSO, ACS, and DFO. The HOA technique does not oscillate on GM and will successfully reach a steady state, resulting in the increase in efficiency of the overall system.

#### 1.3. Organization

## 2. Partial and Complex Partial Shade

## 3. Mathematical Model of the HOA Algorithm

- ${P}_{m}^{iter,age}$ denotes the $mth$ horse position.
- $age$ shows the range of each horse.
- $iter$ describes the current number of iterations.
- $Ve{l}_{m}^{iter,age}$ illustrates the velocity of the vector of that horse.

#### 3.1. Grazing (Gra)

#### 3.2. Hierarchy (H)

#### 3.3. Sociability (Soc)

- $So{c}_{m}^{iter,age}$ describes the vector of social motion that is presented by the $i\mathrm{th}$ horse.
- $so{c}_{m}^{iter,age}$ shows the orientation of that horse in the direction of group $i\mathrm{th}$.
- iter, the iteration is reduced in every cycle, has a parameter of ${\omega}_{s}$.
- $N$ expresses the total number of horses.
- age represents the age range of each horse.

**Figure 9.**Diagram representing grazing, hierarchy, sociability, imitation, defense mechanisms, and roam of the HOA.

#### 3.4. Imitation (Im)

- $I{m}_{m}^{iter,age}$ expresses the vector of motion that represents the $i\mathrm{th}$ horse around the average of the best horse at P position.
- $i{m}_{m}^{iter,age}$ shows the orientation of that horse in the direction of the group on the $i\mathrm{th}$ iteration. This is reduced in every cycle, with a parameter of ${\omega}_{im}$.
- $pN$ represents the number of horses in the best positions, where $p$ is 10% of the selected horses.
- ${\omega}_{im}$ is a reduction factor per cycle for ${i}_{iter}$.

#### 3.5. Defense Mechanism (DefMec)

- $DefMe{c}_{m}^{iter,age}$ describes the escape vector of the$i\mathrm{th}$ horse, based around the average position of a horse in the worst P position.
- $qN$ shows the number of horses in the worst positions, where $q$ is 20% of the total horses.
- ${\omega}_{defmec}$ represents the reduction factor per cycle for iIter that was calculated earlier.

#### 3.6. Roam (Ro)

- The α horses will get the best reactions and also serve as role models for the rest. They take over the coaching role as they begin their hunt for the optimum reaction and develop an exploited strategy. When the characteristics of grazing and defensive mechanisms must be used, this behavior occurs.
- The β horses diligently look for the most likely ideal locations, paying great attention to α.
- The γ horses are created using all their inherent behaviors. They seem to be useful for both the explorative and exploitative phases, even though they exhibit both strong and arbitrary movements.
- Young horses seem to be more rambunctious and livelier, making them more suited to the exploring period.

- The horse herd optimization algorithm (HOA) is a novel MPPT approach that has been developed.
- To collect the GM, the proposed approach needed fewer iterations.
- In PS and CPS situations, the proposed approach shows almost no oscillation and can collect GM.
- Experiments and findings show that the proposed approach with interims of rapid searching and minimal oscillation is preferable.
- A statistical study is performed to determine the algorithm’s efficiency, detecting speed, and steady-state reaction.

- (a)
- Basic configuration: providing variables with a boundary limit and other factors.
- (b)
- Initializing: creating a suitable space with a uniform random selection of horses.
- (c)
- Checking fitness level: determining the cost of each horse, depending on the place and objective function.
- (d)
- Evaluating age: assessing the ages of (α, β, γ, and δ) horses.
- (e)
- Implement the velocity: with respect to every horse’s age, apply the velocity.
- (f)
- Revise the position: updating the position of all horses in the search space.
- (g)
- End: if the stop criteria are not met, go to step (c).

## 4. Tracking Mechanism of HOA

#### HOA under Complex Partial Shading (CPS) Conditions

## 5. Experimental Results

#### 5.1. Case 1: Fast-Changing Irradiance

#### 5.2. Case 2: PS Scenario 1

#### 5.3. Case 3: PS Scenario 2

#### 5.4. Case 4: Complex Partial Shading

Cases | $\mathbf{Irradiance}{\mathbf{S}}_{\mathbf{i}}\left(\frac{\mathbf{k}\mathbf{W}}{{\mathbf{m}}^{2}}\right)$ | ${\mathbf{P}}_{\mathbf{max}}\left(\mathbf{W}\right)$ | |||
---|---|---|---|---|---|

Case4 | PV1 = 0.4 | PV2 = 0.2 | PV3 = 0.6 | PV4 = 0.3 | 1078 |

PV5 = 0.5 | PV6 = 0.4 | PV7 = 0.2 | PV8 = 0.3 | ||

PV9 = 1.00 | PV10 = 0.8 | PV11 = 0.7 | PV12 = 1.0 |

#### 5.5. Efficiency and Performance Evaluation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**The tracking mechanism of the HOA through P-V curve (

**a**) power-time curve, (

**b**) GM tracking curve and (

**c**) voltage-time curve.

Method | Irradiance Scheme | Convergence Time (s) | GM Settle Time (s) | GM Existed | Power at GM | Power Tracking (W) | Energy Value (kWh) | Efficiency (%) |
---|---|---|---|---|---|---|---|---|

DFO | Case 1 | 0.24 | 0.28 | Yes | 1260 | 1259 | 1.66 | 99.9 |

Case 2 PS | 0.26 | 0.43 | Yes | 450 | 448.7 | 0.85 | 99.5 | |

Case 3PS | 0.19 | 0.21 | Yes | 796 | 793.5 | 1.55 | 99.7 | |

Case 4CPS | 0.19 | 0.22 | Yes | 1078 | 1075 | 2.12 | 99.8 | |

HOA | Case 1 | 0.16 | 0.20 | Yes | 1260 | 1259.9 | 1.66 | 99.9 |

Case 2 PS | 0.19 | 0.37 | Yes | 450 | 449.7 | 0.86 | 99.8 | |

Case 3PS | 0.19 | 0.22 | Yes | 796 | 795.8 | 2.12 | 99.9 | |

Case 4CPS | 0.17 | 0.25 | Yes | 1078 | 1077 | 1.65 | 99.8 | |

P&O | Case 1 | 0.12 | 0.12 | Yes | 1260 | 1237 | 0.46 | 98.1 |

Case 2 PS | LM | LM | No | 450 | 220 | 0.47 | 67.7 | |

Case 3PS | LM | LM | No | 796 | 238 | 0.51 | 32.0 | |

Case 4CPS | LM | LM | No | 1078 | 262 | 1.64 | 24.7 | |

PSO | Case 1 | 0.47 | 0.70 | Yes | 1260 | 1257 | 0.83 | 94.6 |

Case 2 PS | 0.41 | 0.81 | Yes | 450 | 439.2 | 1.48 | 97.6 | |

Case 3PS | 0.68 | 0.70 | Yes | 796 | 791.5 | 2.10 | 99.4 | |

Case 4CPS | 0.42 | 0.50 | Yes | 1078 | 1068 | 1.65 | 99.2 | |

ACS | Case 1 | 0.46 | 0.69 | Yes | 1260 | 1258 | 0.83 | 99.8 |

Case 2 PS | 0.30 | 0.84 | Yes | 450 | 420 | 1.49 | 95.5 | |

Case 3PS | 0.35 | 0.45 | Yes | 796 | 778.6 | 2.10 | 97.8 | |

Case 4CPS | 0.40 | 0.56 | Yes | 1078 | 1067 | 3.10 | 99.2 |

Cases | $\mathbf{Irradiance}{\mathbf{S}}_{\mathbf{i}}\left(\frac{\mathbf{k}\mathbf{W}}{{\mathbf{m}}^{2}}\right)$ | ${\mathbf{P}}_{\mathbf{max}}$ | |||
---|---|---|---|---|---|

${\mathrm{C}}_{1-4}$ | PV1 | PV2 | PV3 | PV4 | (W) |

Case1Fast Changing | 1, 0.7, 0.3 | 1, 0.7, 0.3 | 1, 0.7, 0.3 | 1, 0.7, 0.3 | 1260, 880, 380 |

Case2 (Partial Shading) | 0.8 | 0.25 | 0.7 | 0.4 | 449.7 |

Case3 (Partial Shading) | 0.5 | 0.8 | 1.0 | 0.9 | 796.1 |

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**MDPI and ACS Style**

Sarwar, S.; Hafeez, M.A.; Javed, M.Y.; Asghar, A.B.; Ejsmont, K.
A Horse Herd Optimization Algorithm (HOA)-Based MPPT Technique under Partial and Complex Partial Shading Conditions. *Energies* **2022**, *15*, 1880.
https://doi.org/10.3390/en15051880

**AMA Style**

Sarwar S, Hafeez MA, Javed MY, Asghar AB, Ejsmont K.
A Horse Herd Optimization Algorithm (HOA)-Based MPPT Technique under Partial and Complex Partial Shading Conditions. *Energies*. 2022; 15(5):1880.
https://doi.org/10.3390/en15051880

**Chicago/Turabian Style**

Sarwar, Sajid, Muhammad Annas Hafeez, Muhammad Yaqoob Javed, Aamer Bilal Asghar, and Krzysztof Ejsmont.
2022. "A Horse Herd Optimization Algorithm (HOA)-Based MPPT Technique under Partial and Complex Partial Shading Conditions" *Energies* 15, no. 5: 1880.
https://doi.org/10.3390/en15051880